## ERC

The perturbative expansion in quantum field theory describes successfully weakly coupled theories like Quantum Electrodynamics. However, many of the most interesting physical phenomena (nuclei of atoms, magnets or superconductors) are described by strongly coupled field theories. A very successful approach to strongly coupled quantum field theories is the *1/N* expansion. In essence one deals first with a simpler, but still strongly coupled problem: the theory in the large *N* limit. This project builds on the (relatively) recent discovery of a new *1/N* expansion in random tensors and tensor field theories which leads to a new "melonic" large *N* limit. The aim of this project is to study the applications of the melonic limit in instances ranging from theories of random higher dimensional geometries to Conformal Field Theories and from the AdS/CFT correspondence to condensed matter systems.